Question

Косинус²22°30' - синус²22°30' =

Answer 1

= косинус двойного угла

= cos 45° = √2/2 = 1/√2

Answer 2

To find the value of cos²(22°30') - sin²(22°30'), we can use trigonometric identities.

First, let's express 22°30' in radians: 1 degree = π/180 radians 30 minutes = 30/60 degrees = 0.5 degrees = 0.5 * π/180 radians

So, 22°30' = 22 + 0.5 = 22.5 degrees = 22.5 * π/180 radians ≈ 0.3927 radians.

Now, we can use the trigonometric identities:

1. cos(θ) = cos(-θ) and cos(-θ) = cos(θ)
2. sin²(θ) + cos²(θ) = 1

Using these identities:

cos²(22°30') - sin²(22°30') = cos²(0.3927) - sin²(0.3927) = cos²(0.3927) - [1 - cos²(0.3927)] (Using sin²(θ) + cos²(θ) = 1) = cos²(0.3927) - 1 + cos²(0.3927) = 2 * cos²(0.3927) - 1

Now, we can use a calculator to find the value of cos(0.3927) and calculate the final result:

cos(0.3927) ≈ 0.921 cos²(0.3927) ≈ 0.848

So, the final result is:

cos²(22°30') - sin²(22°30') ≈ 2 * 0.848 - 1 ≈ 1.696 - 1 ≈ 0.696.